Find the height of the cyclinder whose radius is 7 cm and the total surface are is ` 1100 cm ^(2)`

Answer

To find the height of the cylinder given its radius and total surface area, we can follow these steps:

### Step 1: Understand the formula for the total surface area of a cylinder
The total surface area (TSA) of a cylinder is given by the formula:
\[ \text{TSA} = 2\pi r (r + h) \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

### Step 2: Substitute the known values into the formula
We know:
- Total Surface Area (TSA) = 1100 cm²
- Radius (r) = 7 cm

Substituting these values into the formula:
\[ 1100 = 2 \pi (7) (7 + h) \]

### Step 3: Simplify the equation
Using \( \pi \approx \frac{22}{7} \):
\[ 1100 = 2 \times \frac{22}{7} \times 7 \times (7 + h) \]
The \( 7 \) in the numerator and denominator cancels out:
\[ 1100 = 2 \times 22 \times (7 + h) \]
This simplifies to:
\[ 1100 = 44 (7 + h) \]

### Step 4: Divide both sides by 44
To isolate \( (7 + h) \):
\[ \frac{1100}{44} = 7 + h \]
Calculating the left side:
\[ 25 = 7 + h \]

### Step 5: Solve for the height (h)
Now, subtract 7 from both sides:
\[ h = 25 - 7 \]
\[ h = 18 \text{ cm} \]

### Final Answer
The height of the cylinder is \( 18 \) cm.

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